In the satellite positioning systems, commonly called GNSS, standing for Global Navigation Satellite System, a fixed or mobile receiver such as a vehicle or an aircraft is located by triangulation by means of a calculation of the distances separating it from a plurality of satellites. The accuracy of the evaluation of distance between the receiver and each of the satellites is a determining factor in the positioning accuracy obtained. The main source of error in the evaluation of this distance is the aggregate delay accumulated by the signal when it passes through the ionosphere, where the partial ionization of the gases at high altitude disturbs the propagation of the signal and results in a variable transmission delay.
It is necessary to be able to have an estimation of the electron content of the Earth's ionosphere, commonly called TEC, standing for Total Electron Content, in order to take into account, for each satellite signal considered, the delay accumulated in passing through the ionosphere. In practice, the receiver calculates its position by integrating a number of corrections of the apparent distances transmitted by the satellites, by means of various integration and filtering techniques. The estimation of the electron content of the ionosphere makes it possible to enhance the accuracy of the calculation of the point (position, speed, time-stamp).
For this, the known GNSS systems can be complemented by so-called augmentation systems which deliver real time corrections linked to the activity of the ionosphere. Augmentation systems based on satellites, commonly called SBAS, standing for Satellite-Based Augmentation System, are used. Such is the case, for example, of the EGNOS system for Europe, which broadcasts, from a plurality of geostationary satellites, correction data to the GPS systems.
Various methods are considered to make it possible to estimate the electron content of the ionosphere and takes its impact into account in the navigation systems. In a known approach, commonly called TRIN model, standing for TRiangular INterpolation, the ionosphere is likened to a thin layer around the terrestrial globe in which is accumulated all of the electron charge of the ionosphere.
The delay of a signal transmitted by a satellite, situated at an altitude above the thin layer, to a receiver situated at a lower altitude than the thin layer, is then estimated by means of the point of intersection of the thin layer with the signal transmission axis, also called line of sight, from the satellite to the receiver. This point is commonly called IPP, standing for Ionosphere Pierce Point. The delay of a signal passing through the thin layer at a given point IPP is determined by means of the vertical total electron content determined at this point for a single-frequency user. The Vertical Total Electron Content, or VTEC, represents the total electron charge of the ionosphere that would have been perceived by a signal passing through this IPP and passing through the thin layer along a vertical axis.
The estimation of the vertical total electron content VTEC makes it possible to establish a mapping of the ionospheric delays in the form of a spherical grid centered on the Earth, situated at altitude and immobile relative to the Earth. The user will then use this grid, commonly called IONO grid, to calculate the ionospheric delay on the lines of sight of each satellite considered, by linear interpolation on this grid. A regular update of the values of the IONO grid, typically every 30 seconds, is broadcast by the SBAS systems to users of the navigation system.
According to one known method, the IONO grid which is accessible to the users of the navigation systems is calculated by interpolation from a second mesh mapping the measurements of the vertical total electron content VTEC. Unlike the IONO grid, this second mesh is not linked to the rotation of the Earth. The second mesh keeps a fixed solar time, the exposure to the sun of each of the nodes of the mesh being constant. The mesh thus becomes independent of the strong changes of the ionospheric layer during a day. In the approach known as TRIN model the second mesh is formed by a regular polyhedron centered on the Earth that has one thousand two hundred and eighty triangular faces. Each of the six hundred and forty-two vertices positioned around the terrestrial globe has an associated evaluation of the vertical total electron content VTEC. FIG. 1 illustrates, in plan view, the meshes of the IONO grid and of the polyhedron of the TRIN model. The nodes of the IONO grid are called IGP, standing for Ionospheric Grid Point, the nodes of the polyhedron of the TRIN model are called TMV, standing for Trin Model Vertex. Typically, the distance 10 separating two IGP nodes is approximately 550 km at the equator, this distance decreasing as a function of latitude. The distance 11 separating two nodes TMV is approximately 950 km.
FIGS. 2.a and 2.b illustrate the principle of the method for estimating the electron content of the ionosphere that is implemented these days for the correction of the navigation systems.
A plurality of receiving beacons 21 situated on the surface of the terrestrial globe 22 picks up a set of signals 23 transmitted by a plurality of navigation satellites 24 situated in orbit. The ionosphere 25 is likened to a thin layer around the terrestrial globe in which is accumulated all of the electron charge. ITL, standing for Ionosphere Thin Layer, denotes the surface, spherical for example, of the thin layer. The vertices TMV of a polyhedron called IPM, standing for Ionosphere Polyhedral Mesh, forms the mesh of the TRIN model. The vertices TMV are positioned on the surface ITL.
It is known that the reception by a beacon 21 of a signal 23 transmitted by a satellite 24 on two frequencies, for example the GPS L1 and GPS L2 frequencies, makes it possible, by a technique known to a person skilled in the art, to determine the distance between the beacon 21 and the satellite 24, as well as the electron content all along the transmission axis of the signal. For more details on this technique, reference can be made to the work entitled “Understanding GPS Principles and Applications”, Elliott D. Kaplan, 2005, Artech House.
According to this technique, it is possible, for each dual-frequency signal 23, to determine an estimation of the vertical total electron content VTEC, for the point IPP of intersection between the transmission axis of the signal 23 and the surface ITL.
As represented in FIG. 2.b, the collection of a set of measurements produced by a plurality of receiving beacons 21 receiving radio frequency signals transmitted by a plurality of transmitting navigation satellites 24 situated in orbit, makes it possible to construct a cloud 26 of points 27 on the surface ITL; each point 27 of the cloud 26 being characterized by spatial coordinates of the IPP and by an estimation of the vertical total electron content VTEC at this point.
In a known method, an estimation of the vertical total electron content VTECi at each of the vertices TMV of the mesh IPM is produced by means of a Kalman filter from a selection of points 27 situated at a distance from the vertex TMV less than a predetermined threshold S.
From this mapping of VTECi values on the mesh IPM, a VTEC mapping is determined on the IONO grid, for example by linear interpolation. This mapping is then made available to the users of the navigation systems, for example by means of the augmentation systems such as EGNOS.
FIGS. 3.a and 3.b illustrate the principle of the method in a simplified case of a one-dimensional distribution. From a distribution of measured VTEC values associated with their abscissa IPP, the method estimates values VTEC1, VTEC2 and VTEC3 for predetermined abscissa x1, x2 and x3 corresponding to the vertices TMV in the simplified case of a one-dimensional mesh.
Typically, the calculation of VTEC2 is constrained by the need to have a straight line pass through the point VTEC1 to the abscissa x1 and another point through the point VTEC3 to the abscissa x3, as well as by the constraint of positioning VTEC2 as close as possible to the point cloud. The method is repeated successively for each of the points along the x-axis. As represented in FIG. 3.b, the estimation of the total electron content for a given abscissa xi by means of the support points x1, x2 and x3 can, depending on the cases, prove relatively far removed from the total electron content measurements. FIGS. 3.a and 3.b illustrate two limitations of the approach currently implemented: the error committed on the estimation of the total electron content on the nodes of the mesh and the non-linearity of the estimation of the total electron content in proximity to the nodes of the mesh.
The method for estimating the electron content of the ionosphere currently implemented allows for a positioning calculation whose accuracy is sufficient when the non-uniformities of the electron content of the ionosphere are small. On the other hand, when the ionosphere exhibits a greater activity, for example during peaks of solar activity, strong amplitude non-uniformities are observed in small geographic surface areas. The existing methods for estimating the ionospheric electron content, such as the TRIN model, do not allow for an estimation that is accurate enough to generate reliable corrections, and allow for a satisfactory positioning by the users of the navigation systems.